Sounds very much like a gasket to me. I ordered one this week from Coffee Parts (one of the sponsor links on the left hand side :) Mine was going much the same. Replaced the gasket and no problems.
As for the millk issue I assume you still have the original steam wand? I would imagine this would be normal due to the wand perhaps sucking a bit of milk up when you turn it off. Ive modded my classic with the silvia wand and it doesnt do that. A good wipe afterwards sorts that out.